\section{Experiments and Results}
\label{sec:results}
In this section, we present our generated model and evaluate its performance.

\subsection{Methodology}
In order to evaluate our model, 
\fix{technically, we cannot evalute our model because we cannot validate it on
test data.}


After we obtained $187$ features as explained in Section we used a high ridge parameter $(10^7)$ to determine the useful features out of these.
We applied the final set of around $50$ features to a 3-fold cross validation model with a grid range of 0 to 100 with steps of 10. 
We then sorted the coefficients learnt in increasing order of their standard errors and p-values and eliminated those that had standard errors higher 
than the coefficients themselves. After we had the newly sorted list we re-ran the cross validation process again to get an estimate of RMSE.
More often than not, the RMSE was lower than what was obtained in the previous run with higher number of features. However several attempts at this finally
enabled us to come up with the original $18$ features that we include in our final model. 
We next increased the number of cross validation folds to 10 and also increased the range of ridge parameter to $100000$ with steps of 100.
Gradual zooming in to the ridge parameter range gave different values of RMSE and finally a range of $0$ to $8000$ yielded a ridge of $160$. 
Any further change of ridge did not change the RMSE which was $8.519$.

The final coefficients are showin in Table. We saw that the features MINRAMNT and MAXRAMNT had a linear relation. 
Including either of them had the same effect on the resulting RMSE and MINRAMNT carried a negative weight whereas 
MAXRAMNT carried a positive weight and including both the features had an adverse effect on the RMSE.
The feature LASTGIFT had a high positive coefficient. We concluded that since someone has a large last donation they are more likely to donate next time,
because probably they can afford it.

However AVGGIFT had a negative coefficien. We concluded that if someone has made a high the average donation till date they will 
be less inclined to continue donating more? From the above two features the conclusion is that if someone has made a high last donation
but whose average donation isn't high (newly started donating large amounts) is more inclined to donate but those who have high average donation will not anymore.

FIXME:

$RFA_2A_E$: Last gift in the range $10-$15. Agrees with the LASTGIFT feature. People with small last donations are less likely to donate again.

$RFA_2A_F$: Last gift in the range $15-$25. Less negative coefficient than the above. So higher the amount of last donation, relatively more likely to pay. But it's still small, so negative coefficient.

Why $RFA_2A_G$ doesn't figure: It the range $\$25$ and above: There are only about 3000 of them in the entire dataset, so after filtering with $TARGET_B=1$, there are very very few and so that is a very biased feature and is removed by remove useless features? (I haven't checked if that is the case...)

$RFA_2F_3$: People who've already gifted 3 times in the last two months are less likely to gift once again?
$RFA_2F_1$: People who've gifted only once in last twelve months have had time to recuperate, and also are likely to gift since they've shown interest once already. This observation, if valid, would reinforce the observation about $NEXTDATE_range9$ above.

Can't think of any of the others...


$NEXTDATE_range9 (93-95)$: This is the date of second gift. Which means they've given a gift before. So, assuming they've been happy enough to continue giving gifts beyond the first one, and that this continuity was pretty recent (november 95), and also long ago enough for them to not feel like "I just gave a gift a month back!" their chances of donating are positive?


